We have a software company and our team is ten people and the number of projects we have is two.
Can one person be the Scrum Master inside two projects at the same time?
It depends a bit on the situation, but from experience I've seen that a full-time, experienced Scrum Master is usually capable of handling two teams. Maybe three if the teams themselves are also highly experienced with Scrum.
Note though that a Scrum Master is in no way attached to a project, but is always attached to a team. If your 10 people are in a single team, then they have a single Scrum Master and they'd be able to handle a dozen projects with their team if that's how many projects the team is working on.
There are no "projects" in Scrum as such, so the guide is pretty much silent on them; it's all about the team. If your Scrum Master has project-based responsibilities instead of team-based responsibilities, your "Scrum Master" doesn't have Scrum Master responsibilities.
Probably, but my experience being the Scrum Master of two teams with greatly different context for nearly half a year was overwhelming. While having two teams on the same context wasn't.
Constantly switching systems and context is not something everyone can handle. So I would recommend it to be sub-optimal and not something for the long-term. Trying to help two different organisational needs and understanding different domain knowledge for two projects can be quite challenging. Certainly if you don't just want to be the Scrum event facilitator.
Having two relative similar projects might work out just fine, but still coaching two teams to become hyper-productive at the same time might not result in the effect that would be possible if you would focus on a single team. Although serving two teams struggling in the same organisation might speed up removing organisational-debt quicker.
It depends also on following factors:
It's not complete list, but gives you some clues.
Here is also similar question with good answers.
It really depends on the context. If everything's going for you, then one scrum master can handle multiple teams (3 or more). The key things that would make this possible are:
You're unlikely to have all of these, but the further away you are from all the items on this list, the more work the scrum master will have to do to support the scrum team making it harder to support multiple teams.
It's worth mentioning (riffing on a comment above - but something of an aside) that according to the guide, scrum doesn't have projects, it has products (and each product has one backlog but may be worked on by multiple teams). Depending on how the business operates, products and projects can be the same or different. For scrum to work, one way or another, the things you need to do for a project will need to make their way into a product backlog. Again, the way this actually happens can vary widely depending on the business. The first point refers to the product.